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A344225 a(n) = Sum_{k=1..n} tau(gcd(k,n)^(n/gcd(k,n))), where tau(n) is the number of divisors of n. 5
1, 3, 4, 8, 6, 17, 8, 23, 17, 35, 12, 57, 14, 61, 44, 74, 18, 123, 20, 121, 72, 137, 24, 215, 47, 187, 96, 217, 30, 387, 32, 261, 152, 311, 100, 488, 38, 385, 204, 441, 42, 813, 44, 505, 294, 557, 48, 961, 93, 739, 332, 697, 54, 1333, 188, 787, 408, 875, 60, 1723, 62, 997, 488, 976, 244, 2433, 68 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{d|n} phi(n/d) * tau(d^(n/d)).

If p is prime, a(p) = 1 + p.

MATHEMATICA

Table[Sum[DivisorSigma[0, GCD[k, n]^(n/GCD[k, n])], {k, n}], {n, 100}] (* Giorgos Kalogeropoulos, May 13 2021 *)

PROG

(PARI) a(n) = sum(k=1, n, numdiv(gcd(k, n)^(n/gcd(k, n))));

(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*numdiv(d^(n/d)));

CROSSREFS

Cf. A344221, A344222, A344223, A344224.

Sequence in context: A330575 A079787 A081307 * A081543 A328876 A105753

Adjacent sequences:  A344222 A344223 A344224 * A344226 A344227 A344228

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 12 2021

STATUS

approved

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Last modified October 24 12:04 EDT 2021. Contains 348225 sequences. (Running on oeis4.)